CN105580016B

CN105580016B - Rotor flux estimator and method of estimating rotor flux

Info

Publication number: CN105580016B
Application number: CN201480052429.3A
Authority: CN
Inventors: Y·唐
Original assignee: Atieva Inc
Current assignee: Atieva Inc
Priority date: 2013-07-23
Filing date: 2014-07-23
Publication date: 2020-07-03
Anticipated expiration: 2034-07-23
Also published as: CN105580016A; EP3025423A4; EP3025423A1; WO2015013361A1; US10521519B2; US20150032423A1

Abstract

A rotor flux estimator is provided. The rotor flux estimator includes an estimation module that generates a first rotor flux vector represented in the phase voltage reference frame and a second rotor flux vector represented in the phase voltage reference frame based on a stator voltage vector represented in the phase voltage reference frame, a rotational speed of the rotor, and a stator current vector represented in the phase voltage reference frame. The estimation module includes at least one processor, and the estimation module includes a rotor flux current model and a rotor flux voltage model.

Description

Rotor flux estimator and method of estimating rotor flux

Technical Field

The invention relates to a rotor flux estimator and a method of estimating rotor flux.

Background

In an induction motor, AC (alternating current) power energizes the windings of the stator, creating a rotating magnetic field characterized by stator flux. The stator flux induces a current in the rotor windings. The rotor experiences torque and rotates under load at a speed that is lower than the rotational speed of the stator flux. The difference between the rotational speed of the rotor and the rotational speed of the stator flux is the slip speed, and the difference between the positions of the rotor and stator flux is referred to as the slip angle. The varying flux seen by the rotor due to the difference in the rotational speed of the stator flux is referred to as the rotor flux.

Two popular types of induction motor controllers, and the algorithms used therein, are Direct Torque Control (DTC) and Field Oriented Control (FOC). in DTC, the coordinates in the stator α and β reference frames are used to control the torque and stator flux, i.e., the coordinates are related to the a, b phase of the stator, where they are calculated in a fixed coordinate system.

Disclosure of Invention

In some embodiments, a rotor flux estimator is provided. The rotor flux estimator includes an estimation module that generates a first rotor flux vector represented in the phase voltage reference frame and a second rotor flux vector represented in the phase voltage reference frame based on a stator voltage vector represented in the phase voltage reference frame, a rotational speed of the rotor, and a stator current vector represented in the phase voltage reference frame. The estimation module includes at least one processor, and the estimation module includes a rotor flux current model and a rotor flux voltage model.

In some embodiments, a rotor flux estimator is provided. The rotor flux estimator includes a first module that generates a first rotor flux vector represented in the phase voltage reference frame from a stator current vector represented in the phase voltage reference frame and a rotational speed of the rotor via application of a rotor flux current model. The rotor flux estimator includes a second module that generates a second rotor flux vector represented in the phase voltage reference frame from a stator voltage vector represented in the phase voltage reference frame, a stator current vector represented in the phase voltage reference frame, and an estimated correction factor by applying a rotor flux voltage model. The rotor flux estimator comprises an estimator regulator that generates an estimated correction factor based on a first rotor flux vector represented in the phase voltage reference frame and a second rotor flux vector represented in the phase voltage reference frame, wherein at least the first module, the second module, or the estimator regulator comprises a processor.

In some embodiments, a method of estimating rotor flux is provided. The method includes generating a first rotor flux vector represented in the phase voltage reference frame by applying a rotor flux current model based on a stator current vector represented in the phase voltage reference frame and a rotational speed of the rotor. The method includes generating a second rotor flux vector represented in the phase voltage reference frame by applying a rotor flux voltage model based on the stator current vector represented in the phase voltage reference frame, the stator voltage vector represented in the phase voltage reference frame, and the estimated correction factor. The method includes generating an estimated correction factor based on a difference between the first rotor flux vector and the second rotor flux vector, wherein at least one method operation is performed by a processor.

Other aspects and advantages of the embodiments will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the described embodiments.

Drawings

The described embodiments and their advantages are best understood by referring to the following description in conjunction with the accompanying drawings. These drawings in no way limit any changes in form and detail that may be made to the described embodiments by one skilled in the art without departing from the spirit and scope of the described embodiments.

Fig. 1 is a schematic diagram of an induction motor controller according to the present invention.

Fig. 2 is a vector diagram illustrating rotation of the longitudinal and transverse axes (d and q) of the stator flux reference frame relative to the x-axis and y-axis of the phase voltage reference frame, as illustrated in the schematic diagram of fig. 1.

Fig. 3 is a schematic diagram of an embodiment of the induction motor controller of fig. 1.

Fig. 4 is a schematic diagram of an embodiment of the flux and torque estimator of fig. 3.

Fig. 5 is a schematic diagram of an embodiment of the flux and torque limiter of fig. 3.

Fig. 6 is a schematic diagram of an embodiment of the torque adjuster of fig. 1 and 3.

Fig. 7 is a schematic diagram of an embodiment of the flux regulator of fig. 1 and 3.

Fig. 8 is a flow chart of a method of estimating rotor flux, which can be implemented in the embodiments of the induction motor controllers in fig. 1 and 3-7.

Detailed Description

Induction motor controllers, embodiments of which are shown in fig. 1-8 and described herein, have features and operations that differ from Field Oriented Control (FOC) and Direct Torque Control (DTC) induction motor controllers. The present induction motor controller performs rotor flux and torque control through a rotor flux regulator circuit and a torque regulator circuit, and operates in a stator flux reference frame and a phase voltage reference frame. The rotor flux and torque regulator loop is (at least partially) processed in a stator flux reference frame. This is in contrast to DTCs that control torque and stator flux, which perform calculations in a static (i.e., non-rotating) reference frame, and to FOC, which perform calculations in a reference frame aligned with the particular flux being controlled, among other differences. Rotor flux is controlled as an adjustable variable in a stator flux reference frame, and in the present system, rotor flux is controlled as an adjustable variable in a rotor flux reference frame or stator flux is controlled as an adjustable variable in a stator flux reference frame, as compared to other systems and methods. In contrast to many (or all) FOC controllers that require current control, embodiments of the present induction motor controller can operate without a current regulation loop.

In the present induction motor controller, the torque regulator and the flux regulator generate a commanded stator voltage vector, which is represented in the stator flux reference frame. This vector is rotated and transformed into a vector in the phase voltage reference frame from which the AC (alternating current) power of the induction motor is derived. Additional modules provide feedback for the torque regulator circuit and the rotor flux regulator circuit, as will also be described further below.

Detailed illustrative embodiments are disclosed herein. However, specific functional details disclosed herein are merely representative for purposes of describing the embodiments. Embodiments may, however, be embodied in many alternate forms and should not be construed as limited to only the embodiments set forth herein.

It will be understood that, although the terms first, second, etc. may be used herein to describe steps or computations, these steps or computations should not be limited by these terms. These terms are only used to distinguish one step or calculation from another. For example, a first calculation may be referred to as a second calculation, and similarly, a second step may be referred to as a first step, without departing from the scope of the present disclosure. As used herein, the term "and/or" and "/" symbol include any and all combinations of one or more of the associated listed items.

As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Thus, the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

It should also be noted that, in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may be executed substantially concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved.

Fig. 1 shows an induction motor controller operating in a stator flux reference frame and a phase voltage reference frame. The induction motor controller provides AC (alternating current) power to the induction motor 106, for example, providing three-phase power to a three-phase induction motor. The torque regulator 108 operates the torque regulator loop 116 and uses this to generate a commanded stator voltage vector projected onto the transverse (q) axis in the stator flux reference frame, which vector projection or component is denoted Vqsc. Rotor flux regulator 110 operates rotor flux regulator circuit 114 and uses this to generate a commanded stator voltage vector projected onto a longitudinal axis (d) in the stator flux reference frame, the vector projection or separation being denoted as Vdds. The stator flux reference frame 102 will be discussed further with respect to fig. 2. The physical quantities in the stator flux reference frame 102 are identified as "dq" if they are vectors, as "d" if they are longitudinal components of vectors, and as "q" if they are transverse components of vectors.

Thus, the torque regulator 108 and the rotor flux regulator 110 together generate the command stator voltage vectors Vdsc, Vqsc, which are represented in the stator flux reference frame 102. Both the torque modulator 108 and the rotor flux modulator 110 operate in the stator flux reference frame 102. In the illustrated embodiment, the torque regulator 108 and the flux regulator 110 are separate modules, but may be combined into a larger module. The commanded stator voltage vectors Vdsc, Vqsc represent the stator voltages, which are commanded by the induction motor controller, which are determined to adjust the torque and rotor flux of the induction motor 106. The DQ/XY coordinate transformation module 112 transforms the commanded stator voltage vectors Vdsc, Vqsc from the stator flux reference frame 102 to the phase voltage reference frame 104, where the transformed vectors Vxsc, Vysc are used to generate AC power for the induction motor 106. In the illustrated embodiment, the induction motor 106 is a three-phase induction motor. The three phases are denoted as a, b, c. Other numbers of phases and other representations of phases may also be used.

The role of fig. 2 is to guide the understanding of the frame of reference, vectors, projections, and embodiments of the induction motor controller described herein. In fig. 2, the x-axis and the y-axis are orthogonal. The x-axis and the y-axis are in a phase voltage reference frame. The x-axis is aligned with one of the phase voltages of the induction motor stator, for example, with the phase voltage of winding "a" of the stator. When AC power is applied to the stator windings, the stator flux linkage (i.e., the total flux linked by the stator windings) rotates relative to the phase voltage reference frame. This is depicted in the vector diagram as the d or longitudinal axis rotating at the rotational speed or rate of Wfs, the rotational speed of the stator flux. As is common practice in the art, the term stator flux linkage is abbreviated stator flux. The q-axis or transverse axis is perpendicular to the d-axis. The q-axis and the d-axis rotate together, which is indicative of the stator flux reference frame rotating relative to the phase voltage reference frame. At any instant, the d-axis is aligned with the stator flux and angularly displaced from the x-axis by a stator flux angle (denoted Afs). Equivalently, the stator flux angle Afs is the angle between the stator flux d-axis and the x-axis. At any instant, any vector physical quantity can be projected to any axis in a stator flux space or a phase voltage space. In the example shown, the rotor currents (denoted ir) are projected onto the d-axis and the q-axis.

In fig. 3, the embodiment of the induction motor controller of fig. 1 is further developed. The induction motor controller in fig. 3 is intended for use in an electric or hybrid vehicle propelled by the induction motor 106. Further embodiments of the induction motor controller may be used in other applications of induction motors than vehicles, for example, in industrial applications, in electromechanical machines and in robots. An overview of the modules, operation, and control loops of the induction motor controller is presented below, followed by a further discussion. It should be appreciated that various variables, coefficients, intermediate values, inputs and outputs may be adjusted to accommodate dimensional compatibility or normalization, modules may be combined or decomposed, or modules may contain additional modules, depending on the implementation and various embodiments.

The vehicle control unit 318, torque command generator 316, and flux command generator 314 cooperate to produce a commanded torque Tc and a commanded rotor flux Frc. Generally, in electric or hybrid vehicles, the commanded torque is based on input from a user, such as the driver of the electric vehicle or the operator of the electromechanical device. More specifically, the commanded torque will be based upon the position of the accelerator pedal and the position of the brake pedal in the vehicle. In other systems these quantities will be based on other inputs.

The command torque Tc and the command rotor magnetic flux Frc are input to the torque regulator 108 and the magnetic flux regulator 110 together with the loop variable. Together, torque regulator 108 and flux regulator 110 derive a commanded stator voltage vector represented in a stator flux reference frame via rotor flux regulator loop 114 and torque regulator loop 116. The rotor flux regulator circuit 114 and the torque regulator circuit 116 are at least partially processed in a stator flux reference frame.

The DQ/XY vector rotation module 302, the space vector modulation module 304, and the DC/AC (direct current to alternating current) inverter 306 process the commanded stator voltage vector to generate AC (alternating current) power for the induction motor 106. The DQ/XY vector rotation module 302 is one embodiment of the DQ/XY coordinate transformation module 112 of fig. 1 that applies vector rotation according to the stator flux angle Afs to transform a commanded stator voltage vector from the stator flux reference frame 102 (e.g., Vdsc, Vqsc) to the phase voltage reference frame 104 (e.g., Vxsc, Vysc). The stator flux angle Afs is estimated rather than sensed and is generated in the flux and torque estimator 310.

The space vector modulation module 304 generates Pulse Width Modulation (PWM) switching control for the DC/AC inverter 306 from the commanded stator voltage vectors Vxsc, Vysc transformed into the phase voltage reference frame 104. The DC/AC inverter 306 generates three-phase AC power for the induction motor 106 according to the pulse width modulated switching control received from the space vector modulation module 304. In further embodiments, the DC/AC inverter 306 generates other numbers of phases of AC power for the induction motor 106 based on the design of the inverter 306 and the induction motor 106.

The flux and torque estimator 310 generates an estimated torque T, an estimated rotor flux angle Afs, an estimated rotor flux Fr, an estimated stator current vector Idqs represented in the stator flux reference frame 102, and an estimated rotor current vector Idqr represented in the stator flux reference frame 102. The flux and torque estimator 310 generates the above quantities from a stator voltage vector vxyz represented in the phase voltage reference system 104, a stator current Iabs of at least two phases, and a rotation speed Wr of the induction motor rotor. In the illustrated embodiment, the rotational speed Wr of the rotor is provided by a sensor, such as a sensor associated with the induction motor 106. For example, the sensor may include or be part of a shaft encoder, tachometer, speedometer, or other sensing device or component. The stator currents may be provided as display currents in all three-phase induction motors 106. However, as is known, providing a two-phase current value allows current to be subtracted in the third phase in a three-phase induction motor, since the vector sum of these three currents is zero (with no net charge build-up or loss from the motor). In one embodiment, the stator currents Iabs are provided by sensors, i.e. measurements.

The estimated rotor flux Fr is coupled from the flux and torque estimator 310 to the flux regulator 110. The estimated torque T is coupled from the flux and torque estimator 310 to the torque regulator 108. The estimated stator flux angle Afs is coupled from the flux and torque estimator 310 to the DQ/XY vector rotation module 302. The space vector modulation module 304 generates a stator voltage vector Vxys represented in the phase voltage reference frame 104 based on the commanded stator voltage vectors Vdsc, Vqsc represented in the stator flux reference frame 102. The stator currents Iabs of at least two phases are provided by the DC/AC inverter 306 and coupled as inputs to the flux and torque estimator 310.

In one embodiment, the flux and torque estimator 310 generates the estimated rotor flux Fr and the estimated torque T using a rotor flux current model and a rotor flux voltage model, as will be further discussed with respect to fig. 4. Referring again to fig. 1, the rotor regulator loop 114 includes an estimated rotor magnetic flux Fr as an input to the flux regulator 110, and the torque regulator loop 116 includes an estimated torque T as an input to the torque regulator 108.

Continuing with fig. 3, the flux and torque limiter 312 operates in conjunction with a flux and command generator 314, a torque command generator 316, and a vehicle control unit 318. The modules cooperate to generate a commanded torque Tc and a commanded rotor flux Frc, the commanded torque Tc is limited to be less than or equal to a variable maximum commanded torque Tcmax, and the commanded rotor flux is limited to be greater than or equal to a variable minimum commanded rotor flux Frcmin and less than or equal to a variable maximum commanded rotor flux Frcmax. The commanded torque Tc is coupled from the torque command generator 316 to the torque regulator 108 as an input thereto. The commanded rotor flux Frc is coupled from flux command generator 314 to both torque generator 108 and flux generator 110 as their inputs. Embodiments of the flux and torque limiter 312 are further discussed with respect to FIG. 5.

The discussion of the induction motor controller of fig. 3 begins with the vehicle control unit 318 and proceeds clockwise (in the figure) around the rotor flux regulator loop and the torque regulator loop. Conceptually, at a high level, the torque command of the induction motor 106 is given by the user through the vehicle control unit 318. The torque command is interpreted according to the state of the induction motor 106 (more specifically, according to the estimated rotor magnetic flux Fr and the estimated torque T of the induction motor 106). From the command torque Tc, the command rotor flux Frc is derived and they are used for calculations or processing in the stator flux reference frame 102. After transformation from the stator flux reference frame 102 to the phase voltage reference frame 104, AC power for the induction motor 106 is generated. The variables are fed back through the rotor flux regulator loop and the torque regulator loop and are used in calculations or processing in the stator flux reference frame 102 to complete the cycle. The variant modules may be made, for example, as hardware, software, firmware, or a combination thereof in various embodiments. For example, in one embodiment, one or more modules are executed in software in a Digital Signal Processor (DSP). Embodiments can include one or more processors, or a combination of one or more processors and hardware.

The vehicle control unit 318 generates an initial command torque Tc0 based on the user input. In one embodiment, the commanded torque Tc0 is mapped from sensors coupled to the throttle and brake pedals of the vehicle. In further embodiments, the command torque Tc0 is calculated, derived, or mapped from other sensors or modules. For example, the increased command torque Tc0 is a result of a user requesting an increase in the speed or acceleration of the vehicle, and the decreased command torque Tc0 is a result of a user requesting a decrease in the speed or acceleration of the vehicle. In some embodiments, the vehicle control unit applies a mapped hysteresis to the command torque Tc 0.

Torque command generator 316 generates command torque Tc based on variable maximum command torque Tcmax and initial command torque Tc 0. The variable maximum command torque Tcmax is applied as a torque limit to the initial command torque Tc 0. This operation may be performed by comparison and mapping, which transmits the initial command torque Tc0 as the command torque Tc unless the initial command torque Tc0 exceeds the variable maximum command torque Tcmax, which is transmitted as the command torque Tc in this case. In various embodiments, the torque command generator 316 operates at the same sampling rate as the main loop sampling rate, or at a slower sampling rate than the main loop sampling rate.

The magnetic flux command generator 314 generates a command rotor magnetic flux Frc from the variable minimum command rotor magnetic flux Frcmin, the variable maximum command torque Tcmax, the command torque Tc, and the rotational speed Wr of the rotor. A variable minimum command rotor flux Frcmin and a variable maximum command torque Tcmax are applied as flux limits to the command rotor flux Frc. In one embodiment, the flux command generator 314 generates an initial command rotor flux, which is directly related to torque, from the command torque Tc using the relationship that the product of the rotational speed Wr of the rotor multiplied by the rotor flux is the back EMF (electromotive force). Induction motors may produce the same given torque by operating a series of different rotor fluxes, where the different rotor fluxes produce different motor operating characteristics, such as different operating efficiencies or different rotor power losses. By real-time calculation or look-up table operation, the initial command rotor flux Frc can be obtained from the command torque Tc, which optimizes certain aspects of system operation (e.g., optimized motor efficiency). A comparison of the initially commanded rotor flux and the flux limit is then performed. The initial command rotor flux Frc is sent as the command rotor flux Frc unless the initial command rotor flux is less than the variable minimum command rotor flux Frcmin, in which case the variable minimum command rotor flux Frcmin is sent as the command rotor flux Frc. If the initial commanded rotor flux is greater than the variable maximum commanded rotor flux Frcmax, the variable maximum commanded rotor flux Frcmax is sent as the commanded rotor flux Frc. In various embodiments, the flux command generator 314 operates at the same sampling rate as the main loop sampling rate, or at a slower sampling rate than the main loop sampling rate.

The torque regulator 108 processes a portion of the torque regulator loop and generates a projection of the commanded stator voltage vector Vqsc on the transverse axis in the stator flux reference frame 102. The torque regulator 108 is processed in the stator flux reference frame 102. Specifically, the torque regulator 108 processes the commanded torque Tc, the estimated torque T, the commanded rotor flux Frc, and the rotational speed Wr of the rotor of the induction motor 106 to produce a commanded stator voltage Vqsc projected onto the transverse axis in the stator flux reference frame 102. In one embodiment, the torque regulator 108 includes a PI (proportional integral) controller. An embodiment of the torque regulator 108 will be further discussed with reference to fig. 6.

Rotor flux modulator 110 processes a portion of the rotor flux modulator circuit and generates a projection of commanded stator voltage vector Vdds onto a longitudinal axis in stator flux reference frame 102. The rotor flux modulator 110 is processed in the stator flux reference frame 102. Specifically, stator flux regulator 110 processes commanded rotor flux Frc and estimated rotor flux Fr to generate a commanded stator voltage Vdsc projected onto the longitudinal axis in stator flux reference frame 102.

The DQ/XY vector rotation module 302, which is a vector rotation module of the stator flux reference frame 102 to the phase voltage reference frame 104, applies the estimated stator flux angle Afs to the commanded stator voltage vectors Vdsc, Vqsc represented in the stator flux reference frame 102. Application of this estimated stator flux angle Afs transforms the commanded stator voltages projected onto the longitudinal and transverse axes from a first vector Vdsc, Vqsc (i.e., a commanded stator voltage vector) in the stator flux reference frame 102 to a second vector Vxsc, Vysc (i.e., a commanded stator voltage vector) in the phase voltage reference frame 104. In one embodiment, the coordinate transformation employs an inverse Clark transformation. In various embodiments, the coordinate transformation is performed using real-time calculations or look-up tables.

The space vector modulation module 304 generates a Pulse Width Modulation (PWM) switching control. Further, the space vector modulation module 304 generates a stator voltage vector vxyz represented in the phase voltage reference frame, as used by the flux and torque estimator 310. The space vector modulation block 304 generates the above quantities from the command stator voltages received from the DQ/XY vector rotation block 302 as second vectors Vxsc, Vysc. In one embodiment, the PWM switching control is standardized. In various embodiments, the stator voltage vector Vxys represented in the phase voltage reference frame 104 is generated by multiplying the supply voltage measurement value Vdc by the commanded stator voltage vectors Vxsc, Vysc represented in the phase voltage reference frame 104, or is measured (e.g., with a sensor) or estimated.

The DC bus 308 provides a supply voltage measurement Vdc from the sensor. In one embodiment, the DC bus is coupled to a battery or battery of the electric vehicle, which provides DC power to the DC/AC inverter 306. In one embodiment, the sensor measures a voltage measurement Vdc of the DC bus 308.

The DC/AC inverter 306 generates three-phase AC power for the induction motor 106 according to the PWM switching control received from the space vector modulation module 304. In one embodiment, the sensor measures the inverter temperature Ti, which is sent to the flux and torque limiter 312. In one embodiment, the sensors measure the stator currents Iabs of at least two phases of the stator and send them to the flux and torque estimator 310.

In the illustrated embodiment, the induction motor 106 is equipped with sensors. One sensor measures the motor temperature Tm and sends it to the flux and torque limiter 312. One sensor measures the rotational speed Wr of the rotor and sends it to the flux and torque estimator 310, flux and torque limiter 312 and flux command generator 314.

The flux and torque estimator 310 generates an estimated stator flux angle Afs for the DQ/XY vector rotation module 302, an estimated rotor flux Fr for the flux regulator 110, an estimated torque for the torque regulator 108, and a stator current vector Idqs represented in the stator flux reference frame 102 and a rotor current vector Idqr represented in the stator flux reference frame 102 for the flux and torque limiter 312. One embodiment of the flux and torque estimator 310 employs two different rotor flux modules, as will be discussed with respect to fig. 4.

The flux and torque limiter 312 generates a variable minimum commanded rotor flux Frcmin, a variable maximum commanded rotor flux Frcmax, and a variable maximum commanded torque Frcmax. The data is generated from the stator current vector Idqs represented in the stator flux reference frame 102, the estimated rotor current vector Idqr represented in the stator flux reference frame 102, the inverter temperature Ti, the motor temperature Tm, the rotational speed Wr of the rotor, and the measured DC voltage Vdc of the DC bus 308. A torque limit, i.e., a variable maximum command torque Tcmax, is sent from flux and torque limiter 312 to torque command generator 316. Smaller and larger rotor flux limits, i.e., a variable minimum commanded rotor flux Frcmin and a variable maximum commanded rotor flux Frcmax, are sent from the flux and torque limiter 312 to the flux command generator 314.

Thus, via the flux and torque estimator 310, the flux regulator 110, and the torque regulator 108, the rotor flux regulator loop 114 and the torque regulator loop 116 are closed and limits are imposed via the flux and torque limiter 312, the flux command generator 314, and the torque command generator 316. To close the loop, allowing feedback back through the phase voltage reference frame 104 to the stator flux reference frame 102, one embodiment of the flux and torque estimator 310 includes a vector rotation module of the phase voltage reference frame to the stator flux reference frame that transforms the current vector from the phase voltage reference frame 104 to the stator flux reference frame 102. Embodiments of the flux and torque limiter 312 will be further discussed with reference to fig. 5.

Fig. 4 illustrates an embodiment of the flux and torque estimator 310. The modules in the flux and torque estimator 310 are implemented in software, hardware, firmware, and various combinations thereof in various embodiments. For example, the modules may be implemented as software modules executed within a DSP or other processor. In various embodiments, rotor flux current model 404, rotor flux voltage model 406, rotor flux calculator 410, rotor current calculator 414, stator flux calculator 412, torque calculator 416, and stator flux angle calculator 418 are based on lookup tables or based on real-time calculations.

The ABC/XY vector rotation module 402, which acts as a stator phase current reference frame to phase voltage reference frame 104 vector rotation module, transforms the stator currents Iabs of at least two phases to a stator current vector Ixys represented in the phase voltage reference frame 104. In one embodiment, the transformation is performed using a park transformation or a variant thereof.

In the embodiment of the flux and torque estimator 310 shown in fig. 4, two rotor flux models cooperate with the modulator to form estimates of the rotor flux vectors. Rotor flux current model 404 converges faster than rotor flux voltage model 406. Combining the two rotor flux models can improve the accuracy of the system over a wide range of operating conditions, that is, over a wide range of motor speeds and a wide range of motor torques. In addition, combining two rotor flux models allows for various voltage, current, and speed based estimates, not just two of the three variables.

Rotor flux current model 404 generates a fast converging estimated rotor flux vector Fxyr represented in phase voltage reference frame 104. The estimated rotor flux vector is generated from a stator voltage vector Ixys represented in the phase voltage reference frame 104 and the rotation speed Wr of the rotor.

Rotor flux voltage model 406 generates a slowly converging estimated rotor flux vector Fxyr0 represented in phase voltage reference frame 104. The model generates an estimated rotor flux vector based on a stator voltage vector vxyz represented in the phase voltage reference frame 104, a stator current vector Ixys represented in the phase voltage reference frame 104, and an estimated correction factor.

Estimated regulator 408 generates an estimated correction factor based on the fast converging estimated rotor flux vector Fxyr represented in phase voltage reference frame 104 and the slow converging estimated rotor flux vector Fxyr0 represented in phase voltage reference frame 104. In one embodiment, the estimation regulator 408 comprises a PI (proportional integral) controller. The PI controller may form an error term based on a difference between the fast converging estimated rotor flux vector Fxyr represented in the phase voltage reference frame 104 and the slow converging estimated rotor flux vector Fxyr represented in the phase voltage reference frame 104. The error term may then be sent to a proportional module and an integral module, the outputs of which are summed to form an estimated correction factor. The PI controller is described with reference to fig. 6 and an embodiment of the torque regulator 108.

Continuing with fig. 4, the computing device using a DSP or other processor or the computing power of a hardware multiplier or one or more look-up tables implements four calculators in the flux and torque estimator 310. The calculators may share power or each may have individual computing power. Rotor flux calculator 410 generates an estimated rotor flux Fr from the fast converging estimated rotor flux vector Fxyr0 represented in the phase voltage reference frame 104. The stator flux calculator 412 generates an estimated stator flux vector Fxys represented in the phase voltage reference frame 104 from the slowly converging estimated rotor flux vector Fxyr0 represented in the phase voltage reference frame 104 and the stator current vector Ixys represented in the phase voltage reference frame 104. In one embodiment, the stator flux calculator 412 includes an inductance model of the stator windings of the induction motor. Rotor current calculator 414 generates a rotor current vector Ixyr represented in the phase voltage reference frame based on the fast converging estimated rotor flux vector Fxyr represented in the phase voltage reference frame 104 and the estimated stator flux vector Fxys represented in the phase voltage reference frame 104. The torque calculator 416 generates an estimated torque T from the stator current vector Ixys represented in the phase voltage reference frame 104 and the estimated stator flux vector Fxys represented in the phase voltage reference frame 104. The stator flux angle calculator 418 generates an estimated stator flux angle Afs from an estimated stator flux vector Fxys represented in the phase voltage reference frame 104.

The XY/DQ vector rotation module 420, which serves as a vector rotation module for the phase voltage reference frame 104 to the stator flux reference frame 102, generates an estimated rotor current vector Idqr represented in the stator flux reference frame 102 and a stator current vector Idqs represented in the stator flux reference frame 102. This module generates the above quantities from the estimated rotor current vector Ixyr represented in the phase voltage reference frame 104, the stator current vector Ixys represented in the phase voltage reference frame 104, and the estimated stator flux angle Afs. In one embodiment, XY/DQ vector rotation module 420 employs a Clark transform.

Fig. 5 illustrates one embodiment of the flux and torque limiter 312. Some modules and flux and torque limiters 312 have a calculator, which may be implemented similar to the calculator in the flux and torque estimator 310. In various embodiments, the modules in the flux and torque limiter 312 are implemented in software, hardware, firmware, and various combinations thereof. In various embodiments, each of the rotor current limiter, the field reducer, the stator current limiter, the low rotor flux limiter, the high rotor flux limiter, the stator-based torque limiter, and the rotor-based torque limiter is based on a lookup table or based on real-time calculations. In various embodiments, the flux and torque limiter 312 operates at the same or slower sampling rate than the main loop sampling rate.

The rotor current limiter 502 generates a variable maximum rotor current Irmax according to the rotational speed Wr of the rotor, an estimated rotor current vector Idqr represented in the stator flux reference frame 102, and the motor temperature Tm. The motor temperature Tm is affected by the rotor current and the rotation speed Wr of the rotor. In one embodiment, the rotor current limiter 502 decreases the variable maximum rotor current Irmax in response to an increasing motor temperature Tm. This action protects the rotor and induction motor 106 from overheating damage due to excessive rotor current. In one embodiment, rotor current limiter 502 comprises a calculator.

The field reducer 504 generates a variable maximum stator flux Fsmax based on the rotational speed Wr of the rotor and the DC voltage Vdc of the DC bus 308 or other power source of the induction motor 106. In one embodiment, field reducer 504 reduces the variable maximum stator flux Fsmax to produce an excess of the base speed in response to the rotational speed Wr of the rotor. The field reducer 504 further reduces the variable maximum stator flux Fsmax in response to the reduced DC voltage of the power supply of the induction motor 106. Some motors become unstable due to excessively high stator flux values. For example, induction motors can easily withstand a maximum stator flux to increase the base speed of the motor, but become unstable at small stator flux values for high rotational speeds. In one embodiment, at higher RPM of the rotor, a low DC voltage reduces the maximum available magnetic flux. As a further example, in some induction motors, for lower supply voltage values, the maximum stator flux should be reduced, over some base value of the rotational speed of the rotor. Various schematic diagrams of field reducer 504 are readily devised in accordance with the characteristics of induction motor 106 specified. In one embodiment, field reducer 504 comprises a calculator.

The stator current limiter 506 generates a variable maximum stator current Ismax from the rotational speed Wr of the rotor, the stator current vector Idqs represented in the stator flux reference frame 102, and the inverter temperature Ti. The inverter temperature Ti is affected by the stator current and the rotation speed Wr of the rotor. In one embodiment, the stator current limiter 506 decreases the variable maximum stator current Ismax in response to an increasing inverter temperature Ti. This protects the stator and induction motor 106 from overheating damage due to excessive stator current.

The low rotor flux limiter 508 generates a variable minimum commanded rotor flux Frcmin based on a variable maximum rotor current Irmax and a rotational speed of the rotor Wr. In one embodiment, low rotor flux limiter 508 sets a variable minimum commanded rotor flux Frcmin consistent with a ready state to accelerate the rotor. For example, because rotor currents are induced in an induction motor, having too low a rotor flux results in a low rotor current, which will give a slow response command to increase the torque of the induction motor. Another reason for setting the variable minimum commanded rotor flux Frcmin is to maintain stability or robustness of the motor against sudden shaft load changes and other disturbances. Setting a minimum commanded rotor flux provides for the induction motor to respond faster to the command, to increase torque and to maintain torque and speed in disturbances. In some embodiments, the minimum value is based on the design and operating environment of the motor.

High rotor flux limiter 510 generates a variable maximum commanded rotor flux Frcmax from a variable maximum stator flux Fsmax and a variable maximum stator current Ismax. In one embodiment, high rotor flux limiter 510 sets a variable maximum commanded rotor flux Frcmax based on a variable maximum stator flux Fsmax and a variable maximum stator current Ismax such that the variable maximum commanded rotor flux Frcmax is reduced in response to the variable maximum stator flux Fsmax or the variable maximum stator current Ismax decreasing.

Stator-based torque limiter 512 generates a variable stator-based maximum command torque Tcmaxs based on a variable maximum stator flux Fsmax and a variable maximum stator current Ismax. In one embodiment, stator-based torque limiter 512 sets a variable stator-based maximum command torque Tcmaxs as a function of the product of a variable maximum stator flux Fsmax and a variable maximum stator current Ismax. In one embodiment, the stator-based torque limiter 512 includes a calculator.

The rotor based torque limiter 514 generates a variable rotor based maximum commanded torque Tcmaxr from the variable maximum rotor current Irmax and the variable maximum commanded rotor flux Frcmax. In one embodiment, the rotor-based torque limiter sets a variable rotor-based maximum commanded torque, Tcmaxr, as a function of the product of a variable maximum rotor current, Irmax, and a variable maximum commanded rotor flux, Frcmax. In one embodiment, the rotor-based torque limiter 514 includes a calculator.

The final torque limiter 516 generates a variable maximum command torque Tcmax based on the variable rotor-based maximum command torque Tcmaxr and the variable stator-based maximum command torque Tcmaxs. In one embodiment, final torque limiter 516 sets a variable rotor-based maximum command torque Tcmax by selecting the lower of the variable rotor-based maximum command torque Tcmaxr and the variable stator-based maximum command torque Tcmaxs. For example, the torque can be calculated from the stator flux and the stator current or from the rotor flux and the rotor current. The results of the two torque calculations are compared and the smaller one is chosen as the torque limit, which is a more conservative choice for stability purposes. In a further embodiment, the larger of the two, the average of the two, or a weighted average of the two may be selected.

Fig. 6 illustrates an embodiment of torque adjuster 108 of fig. 1 and 3. In this embodiment, the torque regulator 108 includes a Proportional Integral (PI) controller 602. The PI controller 602 takes as input the difference between the command torque Tc and the estimated torque T. This difference, the error term in the PI controller terminology, is shown as summing circuit 606 that commands torque Tc as a positive input and estimates torque T as a negative input. The output of the summing circuit 606 produces a torque error. The torque error is routed to a proportional module 614 and an integral module 616, the module 614 generating a factor proportional to the output of the summing circuit 606 (i.e., proportional to the torque error), and the module 616 generating a factor proportional to the integral of the output of the summing circuit 606 (i.e., proportional to the integral of the torque error). The output of the proportional module 614 and the output of the integral module 616 are summed by the summing circuit 608 to produce the output of the PI controller 602.

In the embodiment shown in fig. 6, the torque regulator 108 includes a positive feedback module 604. The positive feedback module 604 includes a summing circuit 610 that takes as input the output of the PI controller 602 and the product of the commanded rotor flux Frc and the rotational speed Wr of the rotor. The positive feedback summation circuit 610 outputs a commanded stator voltage Vqsc projected onto the transverse axis in the stator flux reference frame 102. In a further embodiment, the output summing circuit 608 of the PI controller is combined with the positive feedback summing circuit 610 of the positive feedback module 604 as a single summing circuit of three inputs.

Fig. 7 illustrates an embodiment of the rotor flux modulator 110 of fig. 1 and 3. In this embodiment, rotor flux regulator 110 includes a proportional-integral-derivative (PID) controller 702 having as inputs a commanded rotor flux Frc and an estimated rotor flux Fr, and as an output a commanded stator voltage Vdsc projected onto a longitudinal axis in stator flux reference frame 102. The input summing circuit 704 has the commanded rotor flux Frc as a positive input and the estimated rotor flux Fr as a negative input. In this flux error case, in the terminology of a PID controller, the output of the input summing circuit 704 produces an error term. The flux error is routed to a proportional module 708, an integral module 710, and a derivative module 712, the module 708 producing a term proportional to the output of the summing circuit 704 (i.e., proportional to the flux error), the integral module 710 producing a term proportional to the integral of the output of the summing circuit 704 (i.e., proportional to the integral of the flux error), and the derivative module 712 producing a term proportional to the derivative of the output of the summing circuit 704 (i.e., proportional to the derivative of the flux error). The output of the proportional module 708, the output of the integral module 710, and the output of the derivative module 712 are summed by the output summing circuit 706 to produce the output of the PID controller 702, which is the commanded stator voltage Vdsc projected onto the longitudinal axis in the stator flux reference frame 102.

FIG. 8 illustrates an embodiment of a method of estimating rotor flux. The method may be practiced in the embodiment of the induction motor controller shown in fig. 1 and 3-7. In particular, the method may be practiced in the embodiment of the flux and torque estimator shown in fig. 4 and variations thereof.

From a starting point, in act 802, a first rotor flux vector is generated using a rotor flux current model. For example, the rotor flux current model of fig. 4 may be used to generate an estimated rotor flux vector Fxyr expressed in the phase voltage reference frame from the stator current vector Ixys represented in the phase voltage reference frame and the rotational speed Wr of the rotor.

In act 804, a second rotor flux vector is generated using the rotor flux voltage model. For example, the rotor flux voltage model of fig. 4 may be used to generate an estimated rotor flux vector Fxyr0 represented in the phase voltage reference frame based on a stator voltage vector Vxys represented in the phase voltage reference frame, a stator current vector Ixys represented in the phase voltage reference frame, and an estimated correction factor.

In act 806, an estimated correction factor is generated. For example, the estimator regulator of fig. 4 may be used to generate an estimated correction factor based on the estimated rotor flux vector Fxyr represented in the phase voltage reference frame and the rotor flux vector Fxyr0 represented in the phase voltage reference frame. As a further example, a PI controller may be used to generate the estimated correction factor, such as in connection with the estimator regulator discussed above with respect to fig. 4. In one embodiment, the PI controller generates an integral of a difference between the first rotor flux vector and the second rotor flux vector. The PI controller sums a first term proportional to a difference between the first and second rotor flux vectors and a second term proportional to an integral of the difference between the first and second rotor flux vectors. The estimated correction factor is generated as a result of the summing.

In act 808, the estimated correction factor is applied to generate a second rotor flux vector. For example, the estimated correction factor may be included as an input to the rotor flux voltage model shown in FIG. 4.

In act 810, a rotor magnetic flux is generated. For example, the rotor magnetic flux may be generated by the rotor magnetic flux calculator of fig. 4 from the first rotor magnetic flux vector (i.e., the estimated rotor magnetic flux vector Fxyr represented in the phase voltage reference frame).

In act 812, a stator flux angle is generated. For example, the stator flux angle may be generated via the stator flux calculator and the stator flux angle calculator of fig. 4 based on the stator current vector Ixys represented in the phase voltage reference frame and the second rotor flux vector Fxyr0 represented in the phase voltage reference frame.

In act 814, a torque is generated. For example, torque may be generated via the stator flux calculator and the torque calculator of fig. 4 based on a stator current vector Ixys represented in the phase voltage reference frame and a second rotor flux vector Fxyr0 represented in the phase voltage reference frame.

In act 816, a rotor current vector is generated. For example, the estimated rotor current vector Ixyr represented in the phase voltage reference frame may be generated via the stator flux calculator and rotor current calculator of fig. 4 from the first rotor flux vector Fxyr represented in the phase voltage reference frame, the second rotor flux vector Fxyr0 represented in the phase voltage reference frame, and the stator current vector Ixys represented in the phase voltage reference frame. As a further example, the estimated rotor current vector Idqr represented in the stator flux reference frame may be generated from the estimated rotor current vector Ixyr represented in the phase voltage reference frame, generated as described above and rotated through the XY/DQ vector rotation module of fig. 4.

After act 816, the end point is reached. In a variant, the method operates continuously, steps operate in parallel or branches occur, and so on.

Various embodiments of the present induction motor controller, as described above with reference to fig. 1-8, have some or all of the following features and characteristics. Rotor flux and torque control is performed by a rotor flux regulator loop and a torque regulator loop, rather than a current regulator loop. The rotor flux regulator circuit and the torque regulator circuit are processed in a stator flux reference frame. The physical quantity in the stator flux reference frame is identified as "dq" and the physical quantity in the stator fixed reference frame is identified as "xy".

The flux and torque estimator is followed by a flux and torque limiter. The inputs to the flux and torque estimator are the induced motor phase voltage, the induced or calculated phase voltage, and the induced motor speed. The outputs are the estimated rotor flux, torque magnitude, stator flux angle, and stator and rotor loop currents in the "dq" reference frame. This stator flux angle, relative to the stator fixed reference frame, is used to perform a vector rotation between "dq" and "xy".

The flux and torque limiter operates in real time at the same (or lower) sampling rate as the main loop. The flux and torque limiter determines a maximum torque command and a maximum rotor flux and a minimum rotor flux. The design basis of the limiter block is a comprehensive motor physics model that defines the operating limits of the motor system as a function of the battery bus voltage, the induced motor speed, and the induced inverter and motor operating temperatures.

One of the benefits of flux and torque limiters is that the stator current and the rotor current are limited separately. Under direct torque (in DTC) and under rotor flux control (in FOC) regulators, neither the stator nor rotor currents are directly regulated.

The flux and torque command generator adaptively generates real-time flux and torque commands at the same or a lower sampling rate than the main loop.

One of the benefits of a rotor flux modulator is that the rotor flux generally contains lower harmonics than the stator flux and the air gap flux, thereby improving control accuracy and reducing system jitter. In addition, the phase of the rotor flux lags the stator flux and the air gap flux slightly, which may result in improved system stability and improved peak torque envelope limits.

One of the benefits of processing the main control loop in a frame of reference that is consistent with the stator flux is that the stator flux angle calculation can be more accurate and can converge faster than the rotor flux angle calculation.

With the above embodiments in mind, it should be understood that the embodiments may employ various computer-implemented operations involving data stored in computer systems. The operations are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. Further, performing an operation is often referred to explicitly as producing, identifying, determining, or comparing. Any of the operations described herein that form part of the embodiments are useful machine operations. Embodiments are also directed to an apparatus or device that performs these operations. The apparatus can be specially constructed for the required purposes or the apparatus can be a general purpose computer selectively activated or configured by a computer program stored in the computer. In particular, various general-purpose machines can be used with computer programs written in accordance with the teachings herein, or it can help to construct a more specialized apparatus to perform the required operations.

Embodiments can also be embodied as computer readable code on a computer readable medium. The computer readable medium is any data storage device that can store data which can thereafter be read by a computer system. Examples of the computer readable medium include hard disk drives, Network Attached Storage (NAS), read-only memory, random-access memory, CD-ROMs, CD-R, CD-RWs, magnetic tape, and other optical and non-optical data storage devices. The computer readable medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. The embodiments described herein may be implemented using a variety of computer system architectures including hand-held devices, tablet computers, microprocessor systems, microprocessor-based or programmable consumer electronics, minicomputers, mainframe computers and the like. Embodiments may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a wired or wireless network.

Although the method operations are described in a particular order, it should be understood that other operations may be performed between the operations, the operations may be adjusted so that they occur a slightly different number of times, or the operations may be distributed in a system that allows the processing operations to occur at various intervals relative to the processing.

The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the embodiments and its practical application, to thereby enable others skilled in the art to best utilize the embodiments and various modifications as are suited to the particular use contemplated. Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the invention is not to be limited to the details given herein, but may be modified within the scope and equivalents of the appended claims.

Claims

1. A rotor flux estimator comprising:

an estimation module that generates a first rotor flux vector represented in a phase voltage reference frame and a second rotor flux vector represented in the phase voltage reference frame based on a stator voltage vector represented in the phase voltage reference frame, a rotation speed of a rotor, and a stator current vector represented in the phase voltage reference frame;

the estimation module comprises at least one processor, the estimation module being implemented in hardware or software executing on the at least one processor; and

the estimation module includes a rotor flux current model, a rotor flux voltage model, and an estimator regulator, wherein the estimator regulator includes a proportional integral controller (PI) controller that forms an error term from a difference between the first and second rotor flux vectors, the error term then being sent to a proportional module and an integral module, outputs of the proportional module and the integral module being summed to form an estimated correction factor for the rotor flux voltage model.

2. The rotor flux estimator of claim 1, further comprising:

a stator phase current reference to phase voltage reference vector rotation module that transforms stator currents of at least two phases to the stator current vectors represented in the phase voltage reference.

3. The rotor flux estimator of claim 1, further comprising:

a rotor flux calculator that calculates an estimated rotor flux from the first rotor flux vector.

4. The rotor flux estimator of claim 1, wherein application of the rotor flux current model and the rotor flux voltage model is based on a look-up table.

5. The rotor flux estimator of claim 1, wherein application of the rotor flux current model and the rotor flux voltage model is based on real-time calculations.

6. The rotor flux estimator of claim 1 wherein the rotor flux current model and the rotor flux voltage model cooperate with a regulator in the generation of the second rotor flux vector.

7. The rotor flux estimator of claim 1, wherein the estimation module is implemented in firmware executed on the at least one processor.

8. A rotor flux estimator comprising:

a first module that generates a first rotor flux vector represented in a phase voltage reference frame from a stator current vector represented in the phase voltage reference frame and a rotation speed of a rotor by applying a rotor flux current model;

a second module that generates a second rotor flux vector represented in the phase voltage reference frame from a stator voltage vector represented in the phase voltage reference frame, the stator current vector represented in the phase voltage reference frame, and an estimated correction factor by applying a rotor flux voltage model; and

an estimator regulator comprising a Proportional Integral (PI) controller that forms an error term from a difference between the first rotor flux vector represented in the phase voltage reference frame and the second rotor flux vector represented in the phase voltage reference frame, the error term then being sent to a proportional module and an integral module whose outputs are summed to generate the estimated correction factor, wherein at least one from the group consisting of the first module, the second module, and the estimator regulator comprises a processor.

9. The rotor flux estimator of claim 8, wherein:

the PI controller having the first rotor flux vector and the second rotor flux vector as inputs; and

the PI controller outputs the estimated correction factor.

10. The rotor flux estimator of claim 8 wherein the estimator adjustor comprises:

a difference module that generates a difference between the first rotor flux vector and the second rotor flux vector;

the scaling module generating a first term proportional to the difference between the first and second rotor flux vectors;

the integration module generating a second term proportional to an integration of the difference between the first and second rotor flux vectors; and

a summing module that generates the estimated correction factor as a sum of the first term and the second term.

11. The rotor flux estimator of claim 8, further comprising:

a rotor flux calculator that receives the first rotor flux vector and generates an estimated rotor flux based on a look-up table or real-time calculation.

12. The rotor flux estimator of claim 8, further comprising:

a stator flux calculator that generates a stator flux vector represented in the phase voltage reference frame based on the second rotor flux vector represented in the phase voltage reference frame and the stator current vector represented in the phase voltage reference frame; and

a rotor current calculator that generates a rotor current vector represented in the phase voltage reference frame based on the first rotor flux vector represented in the phase voltage reference frame and the stator flux vector represented in the phase voltage reference frame.

13. The rotor flux estimator of claim 8, further comprising:

a stator flux calculator that generates a stator flux vector represented in the phase voltage reference frame based on the second rotor flux vector represented in the phase voltage reference frame and the stator current vector represented in the phase voltage reference frame, the stator flux calculator including an inductance model of a winding of an induction motor.

14. The rotor flux estimator of claim 8, further comprising:

a torque calculator that generates an estimated torque based on the stator flux vector represented in the phase voltage reference frame and the stator current vector represented in the phase voltage reference frame.

15. The rotor flux estimator of claim 8, further comprising:

a stator flux angle calculator that generates an estimated stator flux angle from the stator flux vector represented in the phase voltage reference frame.

16. A method of estimating rotor flux, performed by a module implemented in hardware or software executing on a processor, the method comprising:

generating a first rotor flux vector represented in a phase voltage reference frame by applying a rotor flux current model based on a stator current vector represented in the phase voltage reference frame and a rotational speed of a rotor;

generating a second rotor flux vector represented in the phase voltage reference frame by applying a rotor flux voltage model based on the stator current vector represented in the phase voltage reference frame, a stator voltage vector represented in the phase voltage reference frame, and an estimated correction factor; and

forming an error term from a difference between the first and second rotor flux vectors, the error term then being sent to a proportional module and an integral module, outputs of which are summed to produce the estimated correction factor, wherein at least one method operation is performed by a processor.

17. The method of claim 16, wherein generating the estimated correction factor comprises:

generating an integral of the difference between the first rotor flux vector and the second rotor flux vector; and

summing a first term proportional to the difference between the first and second rotor flux vectors and a second term proportional to the integral of the difference between the first and second rotor flux vectors.

18. The method of claim 16, further comprising:

generating a rotor magnetic flux from the first rotor magnetic flux vector; and

a stator flux angle is generated from the stator current vector and the second rotor flux vector represented in the phase voltage reference frame.

19. The method of claim 16, further comprising:

torque is generated based on the stator current vector and the second rotor flux vector represented in the phase voltage reference frame.

20. The method of claim 16, further comprising:

a rotor current vector is generated from the stator current vector, the first rotor flux vector and the second rotor flux vector represented in the phase voltage reference frame.

21. The method of claim 16, performed by a module implemented in firmware executing on the processor.